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				<span style="position: absolute;left:15px;bottom:15px;width:90%;"><font class="view-text" style="color:#fcfcfc;font-size:25px">题解 P4464 【[国家集训队] JZPKIL】</font><br><a href="/tags/2021/" class="tag"><span  style="background-color: rgb(52, 152, 219);">2021</span></a>&nbsp;<a href="/tags/莫比乌斯反演/" class="tag"><span  style="background-color: rgb(231, 76, 60);">莫比乌斯反演</span></a>&nbsp;<a href="/tags/Pollard−Rho/" class="tag"><span  style="background-color: rgb(231, 76, 60);">Pollard−Rho</span></a>&nbsp;<a href="/tags/题解/" class="tag"><span  style="background-color: rgb(82, 196, 26);">题解</span></a></span>
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                <h2 id="_1">题意</h2>
<p>给出 <script type="math/tex">n,x,y</script> 求：
<script type="math/tex; mode=display">\sum_{i=1}^n\gcd(i,n)^x\mathrm{lcm}(i,n)^y\bmod {10^9+7}</script>
<script type="math/tex">n\le 10^{18},x,y\le 3000</script>，多组询问</p>
<h2 id="_2">题解</h2>
<p>比较套路，不过还是要 <script type="math/tex">\rm stO</script>出题人。
<script type="math/tex; mode=display">
\begin{aligned}
&\sum_{i=1}^n\gcd(i,n)^x\mathrm{lcm}(i,n)^y\\
=&\sum_{i=1}^n\gcd(i,n)^x(in)^y\gcd(i,n)^{-y}\\
=&n^y\sum_{i=1}^ni^y\gcd(i,n)^{x-y}\\
=&n^y\sum_{d|n}\sum_{i=1}^{\frac nd}(id)^yd^{x-y} [\gcd(i,\frac nd)=1]\\
=&n^y\sum_{d|n}\sum_{i=1}^{\frac nd}i^yd^x \sum_{a|\gcd(i,\frac nd)}\mu(a)\\
=&n^y\sum_{a|n}\mu(a)\sum_{d|\frac na}d^x\sum_{i=1}^\frac{n}{da}(ia)^y\\
=&n^y\sum_{a|n}\mu(a)a^y\sum_{d|\frac na}d^x\sum_{i=1}^\frac{n}{da}i^y
\end{aligned}
</script>
套路地，考虑设 <script type="math/tex">T=da</script>
<script type="math/tex; mode=display">
=n^y\sum_{T|n}\left(\sum_{a|T}\mu(a)a^y\left(\frac{T}{a}\right)^x\right)\left(\sum_{i=1}^\frac nT i^y\right)
</script>
考虑后面的一坨可以看做关于 <script type="math/tex">\frac nT</script> 的 <script type="math/tex">y+1</script> 次多项式</p>
<p>设 <script type="math/tex">F(x)=\sum_{i=1}^xi^y=\sum_{i=0}^{y+1}f_ix^i</script>
<script type="math/tex; mode=display">\begin{aligned}
=&n^y\sum_{T|n}\left(\sum_{a|T}\mu(a)a^y\left(\frac Ta\right)^x\right)\left(\sum_{i=0}^{y+1}f_i\left(\frac nT\right)^i\right)\\
=&n^y\sum_{i=0}^{y+1}f_i\sum_{T|n}\left(\sum_{a|T}\mu(a)a^y\left(\frac Ta\right)^x\right)\left(\frac nT\right)^i\\
\end{aligned}</script>
设 <script type="math/tex">f_1(d)=\mu(d)d^y,f_2(d)=d^x,f_3(d)=d^i</script>
</p>
<p>
<script type="math/tex; mode=display">
=n^y\sum_{i=0}^{y+1}f_i(f_1*f_2*f_3)(n)
</script>
显然 <script type="math/tex">f_1,f_2,f_3</script> 都为积性函数,<script type="math/tex">(f_1*f_2*f_3)</script> 同样为积性函数
<script type="math/tex; mode=display">\begin{aligned}
=&n^y\sum_{i=0}^{y+1}f_i\prod_{p^\alpha|n}(f_1*f_2*f_3)(p^\alpha)\\
=&n^y\sum_{i=0}^{y+1}f_i\prod_{p^\alpha|n}\sum_{a+b+c=\alpha}\mu(p^a)p^{ay}p^{bx}p^{ci}\\
=&n^y\sum_{i=0}^{y+1}f_i\prod_{p^\alpha|n}\sum_{a=0}^1\mu(p^a)p^{ay}\sum_{b=0}^{\alpha-a}p^{bx}p^{(\alpha-a-b)i}\\
\end{aligned}
</script>
关于系数的求法可以参见<a href="ji-lei-shu.html#_1"><script type="math/tex">\color{skyblue}\text{菜鸡の}\mathbb{BLOG}</script></a></p>
<p>不过需要注意伯努利数的多项式是不包括 <script type="math/tex">n^y</script> 次的，要手动加上去。</p>
<p>剩下的就是考验 <script type="math/tex">\rm Pollard-Rho</script> 的常数了。</p>
<h2 id="_3">代码</h2>
<div class="highlight"><pre><span></span><code><span class="linenos" data-linenos="  1 "></span><span class="cp">#include</span><span class="cpf">&lt;bits/stdc++.h&gt;</span><span class="cp"></span>
<span class="linenos" data-linenos="  2 "></span><span class="cp">#define faster</span>
<span class="linenos" data-linenos="  3 "></span><span class="k">namespace</span> <span class="n">in</span><span class="p">{</span>
<span class="linenos" data-linenos="  4 "></span>    <span class="cp">#ifdef faster</span>
<span class="linenos" data-linenos="  5 "></span>    <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">],</span><span class="o">*</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">,</span><span class="o">*</span><span class="n">p2</span><span class="o">=</span><span class="n">buf</span><span class="p">;</span>
<span class="linenos" data-linenos="  6 "></span>    <span class="kr">inline</span> <span class="kt">int</span> <span class="n">getc</span><span class="p">(){</span><span class="k">return</span> <span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="o">&amp;&amp;</span><span class="p">(</span><span class="n">p2</span><span class="o">=</span><span class="p">(</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">)</span><span class="o">+</span><span class="n">fread</span><span class="p">(</span><span class="n">buf</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">,</span><span class="n">stdin</span><span class="p">),</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="o">?</span><span class="nl">EOF</span><span class="p">:</span><span class="o">*</span><span class="n">p1</span><span class="o">++</span><span class="p">;}</span>
<span class="linenos" data-linenos="  7 "></span>    <span class="cp">#else</span>
<span class="linenos" data-linenos="  8 "></span>    <span class="kr">inline</span> <span class="kt">int</span> <span class="n">getc</span><span class="p">(){</span><span class="k">return</span> <span class="nf">getchar</span><span class="p">();}</span>
<span class="linenos" data-linenos="  9 "></span>    <span class="cp">#endif</span>
<span class="linenos" data-linenos=" 10 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">){</span>
<span class="linenos" data-linenos=" 11 "></span>        <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">int</span> <span class="n">f</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">char</span> <span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();</span><span class="k">while</span> <span class="p">(</span><span class="o">!</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span><span class="k">if</span><span class="p">(</span><span class="n">ch</span><span class="o">==</span><span class="sc">&#39;-&#39;</span><span class="p">)</span><span class="n">f</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span><span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();}</span>
<span class="linenos" data-linenos=" 12 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span><span class="n">t</span><span class="o">=</span><span class="n">t</span><span class="o">*</span><span class="mi">10</span><span class="o">+</span><span class="n">ch</span><span class="mi">-48</span><span class="p">;</span><span class="n">ch</span> <span class="o">=</span> <span class="n">getc</span><span class="p">();}</span><span class="k">if</span><span class="p">(</span><span class="n">f</span><span class="p">)</span><span class="n">t</span><span class="o">=-</span><span class="n">t</span><span class="p">;</span>
<span class="linenos" data-linenos=" 13 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 14 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="p">,</span><span class="k">typename</span><span class="p">...</span> <span class="n">Args</span><span class="o">&gt;</span> <span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">,</span> <span class="n">Args</span><span class="o">&amp;</span><span class="p">...</span> <span class="n">args</span><span class="p">){</span><span class="n">read</span><span class="p">(</span><span class="n">t</span><span class="p">);</span><span class="n">read</span><span class="p">(</span><span class="n">args</span><span class="p">...);}</span>
<span class="linenos" data-linenos=" 15 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 16 "></span><span class="k">namespace</span> <span class="n">out</span><span class="p">{</span>
<span class="linenos" data-linenos=" 17 "></span>    <span class="kt">char</span> <span class="n">buffer</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">];</span><span class="kt">int</span> <span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span><span class="k">const</span> <span class="kt">int</span> <span class="n">p2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">)</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 18 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">flush</span><span class="p">(){</span><span class="n">fwrite</span><span class="p">(</span><span class="n">buffer</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">p1</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">stdout</span><span class="p">),</span><span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 19 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">putc</span><span class="p">(</span><span class="k">const</span> <span class="kt">char</span> <span class="o">&amp;</span><span class="n">x</span><span class="p">)</span> <span class="p">{</span><span class="k">if</span><span class="p">(</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="n">flush</span><span class="p">();</span><span class="n">buffer</span><span class="p">[</span><span class="o">++</span><span class="n">p1</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 20 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kt">void</span> <span class="n">write</span><span class="p">(</span><span class="n">T</span> <span class="n">x</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 21 "></span>        <span class="k">static</span> <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">15</span><span class="p">];</span><span class="k">static</span> <span class="kt">int</span> <span class="n">len</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span><span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">){</span><span class="k">do</span><span class="p">{</span><span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;}</span><span class="k">while</span> <span class="p">(</span><span class="n">x</span><span class="p">);}</span><span class="k">else</span><span class="p">{</span><span class="n">putc</span><span class="p">(</span><span class="sc">&#39;-&#39;</span><span class="p">);</span><span class="k">do</span> <span class="p">{</span><span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=-</span><span class="p">(</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="p">)</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;}</span><span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="p">);}</span>
<span class="linenos" data-linenos=" 22 "></span>        <span class="k">while</span> <span class="p">(</span><span class="n">len</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">)</span><span class="n">putc</span><span class="p">(</span><span class="n">buf</span><span class="p">[</span><span class="n">len</span><span class="p">]),</span><span class="o">--</span><span class="n">len</span><span class="p">;</span>
<span class="linenos" data-linenos=" 23 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 24 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 25 "></span><span class="k">using</span> <span class="n">std</span><span class="o">::</span><span class="n">sort</span><span class="p">;</span>
<span class="linenos" data-linenos=" 26 "></span><span class="k">using</span> <span class="n">std</span><span class="o">::</span><span class="n">swap</span><span class="p">;</span>
<span class="linenos" data-linenos=" 27 "></span><span class="k">using</span> <span class="n">std</span><span class="o">::</span><span class="n">__gcd</span><span class="p">;</span>
<span class="linenos" data-linenos=" 28 "></span><span class="k">const</span> <span class="kt">int</span> <span class="n">N</span><span class="o">=</span><span class="mf">6e3</span><span class="o">+</span><span class="mi">100</span><span class="p">;</span>
<span class="linenos" data-linenos=" 29 "></span><span class="k">const</span> <span class="kt">int</span> <span class="n">mod</span><span class="o">=</span><span class="mf">1e9</span><span class="o">+</span><span class="mi">7</span><span class="p">,</span><span class="n">M</span><span class="o">=</span><span class="n">sqrt</span><span class="p">(</span><span class="n">mod</span><span class="p">);</span>
<span class="linenos" data-linenos=" 30 "></span><span class="k">typedef</span> <span class="n">std</span><span class="o">::</span><span class="n">mt19937</span> <span class="n">Random_mt19937</span><span class="p">;</span>
<span class="linenos" data-linenos=" 31 "></span><span class="n">Random_mt19937</span> <span class="nf">rnd</span><span class="p">(</span><span class="n">time</span><span class="p">(</span><span class="mi">0</span><span class="p">));</span>
<span class="linenos" data-linenos=" 32 "></span><span class="kt">long</span> <span class="kt">long</span> <span class="n">factor</span><span class="p">[</span><span class="mi">50</span><span class="p">];</span><span class="kt">int</span> <span class="n">cnt</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos=" 33 "></span><span class="cp">#define ll long long</span>
<span class="linenos" data-linenos=" 34 "></span><span class="cp">#define int __int128</span>
<span class="linenos" data-linenos=" 35 "></span><span class="kt">int</span> <span class="nf">ksm</span><span class="p">(</span><span class="kt">int</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">,</span><span class="kt">int</span> <span class="n">p</span><span class="p">){</span>
<span class="linenos" data-linenos=" 36 "></span>    <span class="kt">int</span> <span class="n">res</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 37 "></span>    <span class="k">while</span><span class="p">(</span><span class="n">b</span><span class="p">){</span>
<span class="linenos" data-linenos=" 38 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">b</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">)</span><span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="o">*</span><span class="n">a</span><span class="o">%</span><span class="n">p</span><span class="p">;</span>
<span class="linenos" data-linenos=" 39 "></span>        <span class="n">a</span><span class="o">=</span><span class="n">a</span><span class="o">*</span><span class="n">a</span><span class="o">%</span><span class="n">p</span><span class="p">,</span><span class="n">b</span><span class="o">&gt;&gt;=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 40 "></span>    <span class="p">}</span><span class="k">return</span> <span class="n">res</span><span class="p">;</span>
<span class="linenos" data-linenos=" 41 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 42 "></span><span class="kr">inline</span> <span class="kt">bool</span> <span class="n">mr</span><span class="p">(</span><span class="n">ll</span> <span class="n">x</span><span class="p">,</span><span class="n">ll</span> <span class="n">b</span><span class="p">){</span>
<span class="linenos" data-linenos=" 43 "></span>    <span class="n">ll</span> <span class="n">k</span><span class="o">=</span><span class="n">x</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 44 "></span>    <span class="k">while</span><span class="p">(</span><span class="n">k</span><span class="p">){</span>
<span class="linenos" data-linenos=" 45 "></span>        <span class="n">ll</span> <span class="n">cur</span><span class="o">=</span><span class="n">ksm</span><span class="p">(</span><span class="n">b</span><span class="p">,</span><span class="n">k</span><span class="p">,</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos=" 46 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">cur</span><span class="o">!=</span><span class="mi">1</span><span class="o">&amp;&amp;</span><span class="n">cur</span><span class="o">!=</span><span class="n">x</span><span class="mi">-1</span><span class="p">)</span><span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
<span class="linenos" data-linenos=" 47 "></span>        <span class="k">if</span><span class="p">((</span><span class="n">k</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">)</span><span class="o">==</span><span class="mi">1</span><span class="o">||</span><span class="n">cur</span><span class="o">==</span><span class="n">x</span><span class="mi">-1</span><span class="p">)</span><span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
<span class="linenos" data-linenos=" 48 "></span>        <span class="n">k</span><span class="o">&gt;&gt;=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 49 "></span>    <span class="p">}</span><span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
<span class="linenos" data-linenos=" 50 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 51 "></span><span class="kr">inline</span> <span class="kt">bool</span> <span class="n">prime</span><span class="p">(</span><span class="n">ll</span> <span class="n">x</span><span class="p">){</span>
<span class="linenos" data-linenos=" 52 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">==</span><span class="mf">46856248255981l</span><span class="n">l</span><span class="o">||</span><span class="n">x</span><span class="o">&lt;</span><span class="mi">2</span><span class="p">)</span>
<span class="linenos" data-linenos=" 53 "></span>        <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
<span class="linenos" data-linenos=" 54 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">==</span><span class="mi">2</span><span class="o">||</span><span class="n">x</span><span class="o">==</span><span class="mi">3</span><span class="o">||</span><span class="n">x</span><span class="o">==</span><span class="mi">7</span><span class="o">||</span><span class="n">x</span><span class="o">==</span><span class="mi">61</span><span class="o">||</span><span class="n">x</span><span class="o">==</span><span class="mi">24251</span><span class="p">)</span>
<span class="linenos" data-linenos=" 55 "></span>        <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
<span class="linenos" data-linenos=" 56 "></span>    <span class="k">return</span> <span class="nf">mr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span><span class="o">&amp;&amp;</span><span class="n">mr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">61</span><span class="p">);</span>
<span class="linenos" data-linenos=" 57 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 58 "></span><span class="kt">int</span> <span class="n">rd</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">){</span><span class="k">return</span> <span class="p">((</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">rnd</span><span class="p">()</span><span class="o">&lt;&lt;</span><span class="mf">16l</span><span class="n">l</span><span class="p">)</span><span class="o">|</span><span class="n">rnd</span><span class="p">())</span><span class="o">%</span><span class="n">x</span><span class="o">+</span><span class="mi">1</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 59 "></span><span class="kt">int</span> <span class="n">f</span><span class="p">(</span><span class="kt">int</span> <span class="n">x</span><span class="p">,</span><span class="kt">int</span> <span class="n">c</span><span class="p">,</span><span class="kt">int</span> <span class="n">n</span><span class="p">){</span>
<span class="linenos" data-linenos=" 60 "></span>    <span class="k">return</span> <span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">c</span><span class="p">)</span><span class="o">%</span><span class="n">n</span><span class="p">;</span>
<span class="linenos" data-linenos=" 61 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 62 "></span><span class="kt">int</span> <span class="n">PR</span><span class="p">(</span><span class="kt">int</span> <span class="n">p</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 63 "></span>    <span class="kt">int</span> <span class="n">k</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="n">x</span><span class="o">=</span><span class="n">rd</span><span class="p">(</span><span class="n">p</span><span class="mi">-1</span><span class="p">),</span><span class="n">y</span><span class="o">=</span><span class="n">x</span><span class="p">,</span><span class="n">d</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">c</span><span class="o">=</span><span class="n">rd</span><span class="p">(</span><span class="mi">99997</span><span class="p">)</span> <span class="p">;</span>
<span class="linenos" data-linenos=" 64 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">d</span><span class="o">==</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos=" 65 "></span>        <span class="n">x</span><span class="o">=</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">c</span><span class="p">,</span><span class="n">p</span><span class="p">);</span>
<span class="linenos" data-linenos=" 66 "></span>        <span class="n">d</span><span class="o">=</span><span class="n">__gcd</span><span class="p">((</span><span class="n">x</span><span class="o">&gt;</span><span class="n">y</span><span class="p">)</span><span class="o">?</span><span class="n">x</span><span class="o">-</span><span class="nl">y</span><span class="p">:</span><span class="n">y</span><span class="o">-</span><span class="n">x</span><span class="p">,</span><span class="n">p</span><span class="p">);</span>
<span class="linenos" data-linenos=" 67 "></span>        <span class="k">if</span><span class="p">(</span><span class="n">i</span><span class="o">==</span><span class="n">k</span><span class="p">)</span><span class="n">y</span><span class="o">=</span><span class="n">x</span><span class="p">,</span><span class="n">k</span><span class="o">&lt;&lt;=</span><span class="mi">1</span><span class="p">;</span> 
<span class="linenos" data-linenos=" 68 "></span>    <span class="p">}</span><span class="k">return</span> <span class="n">d</span><span class="p">;</span>
<span class="linenos" data-linenos=" 69 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 70 "></span><span class="kt">void</span> <span class="n">Gfac</span><span class="p">(</span><span class="kt">int</span> <span class="n">p</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos=" 71 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">p</span><span class="o">==</span><span class="mi">1</span><span class="p">)</span><span class="k">return</span><span class="p">;</span> 
<span class="linenos" data-linenos=" 72 "></span>    <span class="k">if</span><span class="p">(</span><span class="n">prime</span><span class="p">(</span><span class="n">p</span><span class="p">)){</span>
<span class="linenos" data-linenos=" 73 "></span>        <span class="n">factor</span><span class="p">[</span><span class="o">++</span><span class="n">cnt</span><span class="p">]</span><span class="o">=</span><span class="n">p</span><span class="p">;</span>
<span class="linenos" data-linenos=" 74 "></span>        <span class="k">return</span><span class="p">;</span>
<span class="linenos" data-linenos=" 75 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 76 "></span>    <span class="kt">int</span> <span class="n">x</span><span class="o">=</span><span class="n">p</span><span class="p">;</span>
<span class="linenos" data-linenos=" 77 "></span>    <span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="o">==</span><span class="n">p</span><span class="p">)</span><span class="n">x</span><span class="o">=</span><span class="n">PR</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos=" 78 "></span>    <span class="n">Gfac</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="n">Gfac</span><span class="p">(</span><span class="n">p</span><span class="o">/</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos=" 79 "></span><span class="p">}</span>
<span class="linenos" data-linenos=" 80 "></span><span class="cp">#undef int</span>
<span class="linenos" data-linenos=" 81 "></span><span class="k">struct</span> <span class="nc">modint</span><span class="p">{</span>
<span class="linenos" data-linenos=" 82 "></span>    <span class="kt">int</span> <span class="n">x</span><span class="p">;</span>
<span class="linenos" data-linenos=" 83 "></span>    <span class="n">modint</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="o">=</span><span class="mi">0</span><span class="p">){</span><span class="n">x</span><span class="o">=</span><span class="n">o</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 84 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">=</span> <span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 85 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">+=</span><span class="p">(</span><span class="n">modint</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">&gt;=</span><span class="n">mod</span><span class="o">?</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">-</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 86 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">-=</span><span class="p">(</span><span class="n">modint</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">&lt;</span><span class="mi">0</span><span class="o">?</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">+</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 87 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">*=</span><span class="p">(</span><span class="n">modint</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">%</span><span class="n">mod</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 88 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">^=</span><span class="p">(</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span>
<span class="linenos" data-linenos=" 89 "></span>        <span class="n">modint</span> <span class="n">a</span><span class="o">=*</span><span class="k">this</span><span class="p">,</span><span class="n">c</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos=" 90 "></span>        <span class="k">for</span><span class="p">(;</span><span class="n">b</span><span class="p">;</span><span class="n">b</span><span class="o">&gt;&gt;=</span><span class="mi">1</span><span class="p">,</span><span class="n">a</span><span class="o">*=</span><span class="n">a</span><span class="p">)</span><span class="k">if</span><span class="p">(</span><span class="n">b</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">)</span><span class="n">c</span><span class="o">*=</span><span class="n">a</span><span class="p">;</span>
<span class="linenos" data-linenos=" 91 "></span>        <span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">c</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;</span>
<span class="linenos" data-linenos=" 92 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos=" 93 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">/=</span><span class="p">(</span><span class="n">modint</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span> <span class="o">*=</span><span class="n">o</span><span class="o">^=</span><span class="n">mod</span><span class="mi">-2</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 94 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">+=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="o">&gt;=</span><span class="n">mod</span><span class="o">?</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="o">-</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 95 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">-=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="o">&lt;</span><span class="mi">0</span><span class="o">?</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="o">+</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 96 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">*=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">o</span><span class="o">%</span><span class="n">mod</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 97 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">/=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span> <span class="o">*=</span> <span class="p">((</span><span class="n">modint</span><span class="p">(</span><span class="n">o</span><span class="p">))</span><span class="o">^=</span><span class="n">mod</span><span class="mi">-2</span><span class="p">);}</span>
<span class="linenos" data-linenos=" 98 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span> <span class="k">operator</span> <span class="o">+</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">+=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 99 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span> <span class="k">operator</span> <span class="o">-</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">-=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="100 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span> <span class="k">operator</span> <span class="o">*</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">*=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="101 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span> <span class="k">operator</span> <span class="o">/</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">/=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="102 "></span>    <span class="k">friend</span> <span class="n">modint</span> <span class="k">operator</span> <span class="o">^</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">^=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="103 "></span>    <span class="k">friend</span> <span class="kt">bool</span> <span class="k">operator</span> <span class="o">==</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="p">.</span><span class="n">x</span><span class="o">==</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="104 "></span>    <span class="k">friend</span> <span class="kt">bool</span> <span class="k">operator</span> <span class="o">!=</span><span class="p">(</span><span class="n">modint</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="p">.</span><span class="n">x</span><span class="o">!=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="105 "></span>    <span class="kt">bool</span> <span class="k">operator</span> <span class="o">!</span> <span class="p">()</span> <span class="p">{</span><span class="k">return</span> <span class="o">!</span><span class="n">x</span><span class="p">;}</span>
<span class="linenos" data-linenos="106 "></span>    <span class="n">modint</span> <span class="k">operator</span> <span class="o">-</span> <span class="p">()</span> <span class="p">{</span><span class="k">return</span> <span class="n">x</span><span class="o">?</span><span class="n">mod</span><span class="o">-</span><span class="nl">x</span><span class="p">:</span><span class="mi">0</span><span class="p">;}</span>
<span class="linenos" data-linenos="107 "></span>    <span class="n">modint</span> <span class="o">&amp;</span><span class="k">operator</span><span class="o">++</span><span class="p">(</span><span class="kt">signed</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span><span class="o">+=</span><span class="mi">1</span><span class="p">;}</span>
<span class="linenos" data-linenos="108 "></span><span class="p">};</span>
<span class="linenos" data-linenos="109 "></span><span class="n">modint</span> <span class="n">fac</span><span class="p">[</span><span class="n">N</span><span class="p">],</span><span class="n">ifac</span><span class="p">[</span><span class="n">N</span><span class="p">],</span><span class="n">F</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
<span class="linenos" data-linenos="110 "></span><span class="n">modint</span> <span class="n">B</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
<span class="linenos" data-linenos="111 "></span><span class="n">modint</span> <span class="nf">C</span><span class="p">(</span><span class="kt">int</span> <span class="n">n</span><span class="p">,</span><span class="kt">int</span> <span class="n">m</span><span class="p">){</span><span class="k">if</span><span class="p">(</span><span class="n">m</span><span class="o">&gt;</span><span class="n">n</span><span class="p">)</span><span class="k">return</span> <span class="mi">0</span><span class="p">;</span><span class="k">return</span> <span class="n">fac</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">*</span><span class="n">ifac</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="o">*</span><span class="n">ifac</span><span class="p">[</span><span class="n">n</span><span class="o">-</span><span class="n">m</span><span class="p">];}</span>
<span class="linenos" data-linenos="112 "></span><span class="kt">signed</span> <span class="nf">main</span><span class="p">(){</span>
<span class="linenos" data-linenos="113 "></span>    <span class="c1">//freopen(&quot;JZPKIL.in&quot;,&quot;r&quot;,stdin);</span>
<span class="linenos" data-linenos="114 "></span>    <span class="c1">//freopen(&quot;JZPKIL.out&quot;,&quot;w&quot;,stdout); </span>
<span class="linenos" data-linenos="115 "></span>    <span class="n">fac</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">N</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="n">fac</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">=</span><span class="n">fac</span><span class="p">[</span><span class="n">i</span><span class="mi">-1</span><span class="p">]</span><span class="o">*</span><span class="n">i</span><span class="p">;</span>
<span class="linenos" data-linenos="116 "></span>    <span class="n">ifac</span><span class="p">[</span><span class="n">N</span><span class="mi">-1</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="o">/</span><span class="n">fac</span><span class="p">[</span><span class="n">N</span><span class="mi">-1</span><span class="p">];</span><span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="n">N</span><span class="mi">-1</span><span class="p">;</span><span class="n">i</span><span class="p">;</span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="n">ifac</span><span class="p">[</span><span class="n">i</span><span class="mi">-1</span><span class="p">]</span><span class="o">=</span><span class="n">ifac</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">i</span><span class="p">;</span>
<span class="linenos" data-linenos="117 "></span>    <span class="n">B</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="118 "></span>    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">m</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">m</span><span class="o">&lt;=</span><span class="mi">3000</span><span class="p">;</span><span class="n">m</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="119 "></span>        <span class="n">modint</span> <span class="n">tmp</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="120 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">m</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="121 "></span>            <span class="n">tmp</span><span class="o">+=</span><span class="n">C</span><span class="p">(</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">i</span><span class="p">)</span><span class="o">*</span><span class="n">B</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<span class="linenos" data-linenos="122 "></span>        <span class="n">B</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="o">=-</span><span class="n">tmp</span><span class="o">/</span><span class="n">C</span><span class="p">(</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">m</span><span class="p">);</span>
<span class="linenos" data-linenos="123 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="124 "></span>    <span class="kt">int</span> <span class="n">t</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="125 "></span>    <span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">t</span><span class="p">);</span>
<span class="linenos" data-linenos="126 "></span>    <span class="k">while</span><span class="p">(</span><span class="n">t</span><span class="o">--</span><span class="p">){</span>
<span class="linenos" data-linenos="127 "></span>        <span class="kt">long</span> <span class="kt">long</span> <span class="n">n</span><span class="o">=</span><span class="mi">970436691605084065</span><span class="p">;</span><span class="kt">int</span> <span class="n">x</span><span class="o">=</span> <span class="mi">2312</span><span class="p">,</span><span class="n">y</span><span class="o">=</span> <span class="mi">2977</span><span class="p">;</span>
<span class="linenos" data-linenos="128 "></span>        <span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">);</span>
<span class="linenos" data-linenos="129 "></span>        <span class="n">cnt</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">Gfac</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
<span class="linenos" data-linenos="130 "></span>        <span class="n">sort</span><span class="p">(</span><span class="n">factor</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">factor</span><span class="o">+</span><span class="mi">1</span><span class="o">+</span><span class="n">cnt</span><span class="p">);</span>
<span class="linenos" data-linenos="131 "></span>        <span class="n">modint</span> <span class="n">Inv</span><span class="o">=</span><span class="n">modint</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">y</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
<span class="linenos" data-linenos="132 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">y</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="133 "></span>            <span class="n">F</span><span class="p">[</span><span class="n">y</span><span class="o">-</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">C</span><span class="p">(</span><span class="n">y</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">i</span><span class="p">)</span><span class="o">*</span><span class="n">B</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">Inv</span><span class="p">;</span>
<span class="linenos" data-linenos="134 "></span>        <span class="n">F</span><span class="p">[</span><span class="n">y</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
<span class="linenos" data-linenos="135 "></span>        <span class="n">modint</span> <span class="n">ans</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="136 "></span>        <span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="137 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">y</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="138 "></span>            <span class="n">modint</span> <span class="n">res</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="139 "></span>            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">l</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">l</span><span class="o">&lt;=</span><span class="n">cnt</span><span class="p">;</span><span class="n">l</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="140 "></span>                <span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="n">l</span><span class="p">;</span><span class="k">while</span><span class="p">(</span><span class="n">factor</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">==</span><span class="n">factor</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="o">&amp;&amp;</span><span class="n">j</span><span class="o">&lt;=</span><span class="n">cnt</span><span class="p">)</span><span class="n">j</span><span class="o">++</span><span class="p">;</span>
<span class="linenos" data-linenos="141 "></span>                <span class="kt">int</span> <span class="n">alpha</span><span class="o">=</span><span class="n">j</span><span class="o">-</span><span class="n">l</span><span class="p">;</span><span class="kt">long</span> <span class="kt">long</span> <span class="n">p</span><span class="o">=</span><span class="n">factor</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="o">%</span><span class="n">mod</span><span class="p">;</span><span class="n">l</span><span class="o">=</span><span class="n">j</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos="142 "></span>                <span class="n">modint</span> <span class="n">tmp</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="143 "></span>
<span class="linenos" data-linenos="144 "></span>                    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">a</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">a</span><span class="o">&lt;=</span><span class="mi">1</span><span class="p">;</span><span class="n">a</span><span class="o">++</span><span class="p">){</span>
<span class="linenos" data-linenos="145 "></span>                        <span class="k">if</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="mi">0</span><span class="p">){</span>
<span class="linenos" data-linenos="146 "></span>                            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">b</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">b</span><span class="o">&lt;=</span><span class="n">alpha</span><span class="o">-</span><span class="n">a</span><span class="p">;</span><span class="n">b</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="147 "></span>                                <span class="c1">//tmp+=(modint(p)^b*x)*(1-(modint(p)^i*(alpha-a-b+1)))/(1-(modint(p)^i));</span>
<span class="linenos" data-linenos="148 "></span>                                <span class="c1">//for(int c=0;c&lt;=alpha-a-b;c++)</span>
<span class="linenos" data-linenos="149 "></span>                                <span class="c1">//  tmp+=(modint(p)^b*x)*(modint(p)^c*i);</span>
<span class="linenos" data-linenos="150 "></span>                                <span class="n">tmp</span><span class="o">+=</span><span class="p">(</span><span class="n">modint</span><span class="p">(</span><span class="n">p</span><span class="p">)</span><span class="o">^</span><span class="n">b</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">i</span><span class="o">*</span><span class="p">(</span><span class="n">alpha</span><span class="o">-</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">));</span>
<span class="linenos" data-linenos="151 "></span>                        <span class="p">}</span><span class="k">else</span><span class="p">{</span>
<span class="linenos" data-linenos="152 "></span>                            <span class="n">modint</span> <span class="n">kk</span><span class="o">=-</span><span class="p">(</span><span class="n">modint</span><span class="p">(</span><span class="n">p</span><span class="p">)</span><span class="o">^</span><span class="n">y</span><span class="p">);</span>
<span class="linenos" data-linenos="153 "></span>                            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">b</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">b</span><span class="o">&lt;=</span><span class="n">alpha</span><span class="o">-</span><span class="n">a</span><span class="p">;</span><span class="n">b</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="154 "></span>                                <span class="c1">//tmp+=kk*(modint(p)^b*x)*(1-(modint(p)^i*(alpha-a-b+1)))/(1-(modint(p)^i));</span>
<span class="linenos" data-linenos="155 "></span>                                <span class="c1">//for(int c=0;c&lt;=alpha-a-b;c++)</span>
<span class="linenos" data-linenos="156 "></span>                                <span class="c1">//  tmp+=kk*(modint(p)^b*x)*(modint(p)^c*i);</span>
<span class="linenos" data-linenos="157 "></span>                                <span class="n">tmp</span><span class="o">+=</span><span class="n">kk</span><span class="o">*</span><span class="p">(</span><span class="n">modint</span><span class="p">(</span><span class="n">p</span><span class="p">)</span><span class="o">^</span><span class="n">b</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">i</span><span class="o">*</span><span class="p">(</span><span class="n">alpha</span><span class="o">-</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">));</span>
<span class="linenos" data-linenos="158 "></span>                        <span class="p">}</span>
<span class="linenos" data-linenos="159 "></span>                    <span class="p">}</span>
<span class="linenos" data-linenos="160 "></span>                <span class="n">res</span><span class="o">*=</span><span class="n">tmp</span><span class="p">;</span>
<span class="linenos" data-linenos="161 "></span>            <span class="p">}</span>
<span class="linenos" data-linenos="162 "></span>            <span class="n">ans</span><span class="o">+=</span><span class="n">res</span><span class="o">*</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<span class="linenos" data-linenos="163 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="164 "></span>        <span class="n">ans</span><span class="o">*=</span><span class="n">modint</span><span class="p">(</span><span class="n">n</span><span class="o">%</span><span class="n">mod</span><span class="p">)</span><span class="o">^</span><span class="n">y</span><span class="p">;</span>
<span class="linenos" data-linenos="165 "></span>        <span class="n">out</span><span class="o">::</span><span class="n">write</span><span class="p">(</span><span class="n">ans</span><span class="p">.</span><span class="n">x</span><span class="p">);</span>
<span class="linenos" data-linenos="166 "></span>        <span class="n">out</span><span class="o">::</span><span class="n">putc</span><span class="p">(</span><span class="sc">&#39;\n&#39;</span><span class="p">);</span>
<span class="linenos" data-linenos="167 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="168 "></span>    <span class="n">out</span><span class="o">::</span><span class="n">flush</span><span class="p">();</span>
<span class="linenos" data-linenos="169 "></span><span class="p">}</span>
</code></pre></div>
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